Published: May 23, 2022
Citation: Publicationes Mathematicae Debrecen vol. 100, no. 3-4, article no. 12 (May 2022) pp. 449-460
Author(s)
Abhishek Juyal (The Institute of Mathematical Sciences), Dustin Moody (NIST)
A Heron triangle is one in which the side lengths and area are integers. An integral right triangle is an example of a Heron triangle. In this paper, we show that there are infinitely many pairs of integral right triangles and Heron triangles with a common area and common perimeter, continuing a line of similar results with other pairs of geometric shapes. This result is established using the theory of elliptic curves.
A Heron triangle is one in which the side lengths and area are integers. An integral right triangle is an example of a Heron triangle. In this paper, we show that there are infinitely many pairs of integral right triangles and Heron triangles with a common area and common perimeter, continuing a...
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A Heron triangle is one in which the side lengths and area are integers. An integral right triangle is an example of a Heron triangle. In this paper, we show that there are infinitely many pairs of integral right triangles and Heron triangles with a common area and common perimeter, continuing a line of similar results with other pairs of geometric shapes. This result is established using the theory of elliptic curves.
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Keywords
elliptic curve; right triangle; Heron triangle; parallelogram; common area; common perimeter
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